2/5 + 1/5 + 1/x = 1
x = 5/2
x = 5/2
Alice's work rate = 1 job / 5 hours = 1/5 job per hour
Next, we know that Alice worked on the job for 2 hours before her friend joined. Therefore, Alice completed:
Alice's work done = Alice's work rate * time worked
Alice's work done = (1/5 job per hour) * 2 hours
Alice's work done = 2/5 job
Since Alice and her friend together completed the job in 1 hour, Alice's friend must have completed the remaining work, which is:
Friend's work done = Total work - Alice's work done
Friend's work done = 1 job - 2/5 job
Friend's work done = 3/5 job
Now, we can find out how long it would take Alice's friend to complete the job on her own. We'll let x represent the time it takes for the friend to complete the job:
Friend's work rate = Friend's work done / time taken
Friend's work rate = (3/5 job) / x hours
We are given the equation 1 + 1/5 = 1/x, which represents the combined work rate of Alice and her friend working together.
1 + 1/5 = 1/x
To solve this equation for x, we can cross-multiply:
5(1) + (1) = 5(1/x)
5 + 1 = 5/x
6 = 5/x
Now, we can solve for x by cross-multiplying again:
6x = 5
Dividing both sides by 6:
x = 5/6
Therefore, it would take Alice's friend 5/6 of an hour (or 50 minutes) to complete the entire job on her own.